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A073340 Fibonacci prime pairs: the indices of each pair differ by two and the relevant Fibonacci numbers are both prime. 3
3, 5, 5, 7, 11, 13, 431, 433, 569, 571 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are no other Fibonacci prime pairs up to Fibonacci[104911]. (See A001605.) Are there any larger terms?

REFERENCES

David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 46 (Rev. ed. 1997)

LINKS

Table of n, a(n) for n=1..10.

EXAMPLE

The 431st Fibonacci number and the 433rd Fibonacci number are both prime and their indices differ by 2.

MATHEMATICA

Flatten[Select[Partition[Select[Range[3000], PrimeQ[Fibonacci[ # ]]&], 2, 1], #[[2]] - #[[1]] == 2 &]]

PROG

(Python)

from sympy import isprime

def afind(limit):

  i, fnm2, fnm1 = 1, 1, 1

  while i < limit:

    if isprime(fnm2) and isprime(fnm2 + fnm1):

      print(i, i+2, sep=", ", end=", ")

    i, fnm2, fnm1 = i+1, fnm1, fnm2 + fnm1

afind(600) # Michael S. Branicky, Mar 05 2021

CROSSREFS

Cf. A000045, A001605, A279795, A281087.

Sequence in context: A069201 A272882 A077800 * A118409 A162779 A158284

Adjacent sequences:  A073337 A073338 A073339 * A073341 A073342 A073343

KEYWORD

more,nonn

AUTHOR

Harvey P. Dale, Aug 25 2002

EXTENSIONS

Offset changed to 1 by Joerg Arndt, Jan 18 2017

a(1) and a(2) prepended by Bobby Jacobs, Jan 18 2017

STATUS

approved

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Last modified April 14 05:00 EDT 2021. Contains 342941 sequences. (Running on oeis4.)